Wal-Mart Stores Inc. is making a play for the used videogame business, a move that could bring in new customers while rankling GameStop Corp., which has long dominated the market.

Starting next week, the world's largest retailer will allow shoppers to trade in used videogames for anything from groceries to gadgets across 3,100 of its stores. Customers will receive gift cards ranging from a few dollars to more than $35, based on the...